This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A291916 #36 Feb 16 2025 08:33:51
%S A291916 4,6,11,19,34,60,106,186,325,565,978,1686,2896,4958,8463,14407,24466,
%T A291916 41456,70102,118322,199369,335401,563426,945194,1583644,2650230,
%U A291916 4430291,7398331,12342850,20573220,34262338,57013866,94800781,157517533,261545778,433993662
%N A291916 Number of (not necessarily maximal) cliques in the n-Fibonacci cube graph.
%H A291916 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Clique.html">Clique</a>
%H A291916 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciCubeGraph.html">Fibonacci Cube Graph</a>
%H A291916 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,1,1).
%F A291916 a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5).
%F A291916 G.f.: (x (-4 + 6 x + 3 x^2 - 4 x^3 - 2 x^4))/((-1 + x) (-1 + x + x^2)^2).
%F A291916 a(n) = (n*Lucas(n + 1) + Lucas(n + 4) - Fibonacci(n - 3))/5 + 1. - _Ehren Metcalfe_, Oct 16 2017
%t A291916 LinearRecurrence[{3, -1, -3, 1, 1}, {4, 6, 11, 19, 34}, 20]
%t A291916 Table[((25 - 19 Sqrt[5]) (1 - Sqrt[5])^n + (1 + Sqrt[5])^n (25 + 19 Sqrt[5]))/(25 2^(n + 1)) + n LucasL[n + 1]/5 + 1, {n, 20}] // Expand
%t A291916 CoefficientList[Series[(-4 + 6 x + 3 x^2 - 4 x^3 - 2 x^4)/((-1 + x) (-1 + x + x^2)^2), {x, 0, 20}], x]
%t A291916 Table[(n LucasL[n + 1] + LucasL[n + 4] - Fibonacci[n - 3])/5 + 1, {n, 40}] (* _Eric W. Weisstein_, Nov 29 2017 *)
%Y A291916 Cf. A022137, A001629 (maximum and maximal cliques).
%K A291916 nonn
%O A291916 1,1
%A A291916 _Eric W. Weisstein_, Sep 05 2017